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"The central theme of the book is easily stated. It is that many simple rules can lead to complex behavior. The example that is used repeatedly to illustrate this theme is a favorite toy of complexity theorists known as the cellular automaton, so I will have to say a bit about what cellular automata are.

Take a piece of white graph paper that has been cross-hatched into little squares. These are the "cells." Blacken one or more of the cells in the top row, chosen any way you like, leaving all the others white. This is your input. Now blacken some cells in the second row, according to some fixed rule that tells you to make any cell black or leave it white depending on the colors of its three neighboring cells in the first row (that is, the cells in the first row that are either immediately above the cell in the second row or one cell over to the right or left.) Then use the same rule, whatever it is, automatically to color each cell in the third row according to the colors of its three neighboring cells in the second row, and keep going automatically in the same way to the rows below. The coloring rule used in this way is an elementary cellular automaton.

This may seem like a solitaire variation on tick-tack-toe, only not as exciting. Indeed, most of the 256 possible[2] elementary cellular automata of this sort are pretty boring. For instance, consider rule 254, which dictates that a cell is made black if the cell immediately above it, or above it and one space over to the left or right, is black, and otherwise it is left white. Whatever the input pattern of black cells in the top row, the black cells will spread in the rows below, eventually filling out an expanding black triangle, so that the cells in any given column will all be black once you get to a low-enough row.

But wait. Wolfram's prize automaton is number 110 in his list of 256. Rule 110 dictates that a cell in one row is left white if the three neighboring cells in the row above are all black or all white or black-white-white, and otherwise it is made black. Figure A shows the result of applying this rule twenty times with a very simple input, in which just one cell is made black in the top row. Not much happening here. Wolfram programmed a computer to run this automaton, and he ran it for millions of steps. After a few hundred steps something surprising happened: the rule began to produce a remarkably rich structure, neither regular nor completely random. The result after 700 steps is shown in Figure B. A pattern of black cells spreads to the left, with a foamy strip furthest to the left, then a periodic alternation of regions of greater and lesser density of black cells which moves to the right, followed by a jumble of black and white cells. It is a dramatic demonstration of Wolfram's conclusion, that even quite simple rules and inputs can produce complex behavior."

    -REVIEW: of A New Kind of Science (Steven Weinberg, NY Review of Books)

Let us suppose for a moment that all religion is a wholly human creation with no basis in reality. Given the seeming complexity of the world around us, it is hardly surprising that early man should have been pantheistic, believing that the myriad wonders around him must have been driven by a corresponding plethora of powers. But monotheism proposes a more radical hypothesis, that there is a single Creator and/or Creation moment, a moment of surpassing simplicity as regards our universe. In fact, the King James version of the Bible renders this moment in a way that is especially germane to Mr. Wolfram's theory:
In the beginning was the Word, and the Word was with God, and the Word was God.
    -Gospel According to John, 1:1
So the Creation of the Universe begins with a word, The Word. And all the complexity around us is a function of one being and a few simple commands:
1: In the beginning God created the heaven and the earth.
2: And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
3: And God said, Let there be light: and there was light.
4: And God saw the light, that it was good: and God divided the light from the darkness.
5: And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
6: And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.
7: And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so.
8: And God called the firmament Heaven. And the evening and the morning were the second day.
9: And God said, Let the waters under the heaven be gathered together unto one place, and let the dry land appear: and it was so.
10: And God called the dry land Earth; and the gathering together of the waters called he Seas: and God saw that it was good.
11: And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so.
12: And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good.
13: And the evening and the morning were the third day.
14: And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years:
15: And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so.
16: And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also.
17: And God set them in the firmament of the heaven to give light upon the earth,
18: And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good.
19: And the evening and the morning were the fourth day.
20: And God said, Let the waters bring forth abundantly the moving creature that hath life, and fowl that may fly above the earth in the open firmament of heaven.
21: And God created great whales, and every living creature that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good.
22: And God blessed them, saying, Be fruitful, and multiply, and fill the waters in the seas, and let fowl multiply in the earth.
23: And the evening and the morning were the fifth day.
24: And God said, Let the earth bring forth the living creature after his kind, cattle, and creeping thing, and beast of the earth after his kind: and it was so.
25: And God made the beast of the earth after his kind, and cattle after their kind, and every thing that creepeth upon the earth after his kind: and God saw that it was good.
26: And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.
27: So God created man in his own image, in the image of God created he him; male and female created he them.
28: And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.
29: And God said, Behold, I have given you every herb bearing seed, which is upon the face of all the earth, and every tree, in the which is the fruit of a tree yielding seed; to you it shall be for meat.
30: And to every beast of the earth, and to every fowl of the air, and to every thing that creepeth upon the earth, wherein there is life, I have given every green herb for meat: and it was so.
31: And God saw every thing that he had made, and, behold, it was very good. And the evening and the morning were the sixth day.
    -Genesis, 1:1-31
Now, even if this is all merest metaphor, it is the most powerful and enduring metaphor of our species, and so, though reason may have long since killed off God, rationalism/science has never slackened in its quest for the unified theories and even the moments of simplicity that will explain the Universe. Thus, Darwinism derives its power not from any basis in observable science but from the idea that all life can be traced back to one organism. Thus, even as he made the laws of physics seem more complicated, Einstein believed that there must be a simple Unified Theory that would explain all: "God does not play dice with the Universe." And today his successors seek a "God particle" that will help them understand the single moment of Creation. All of them depend on the idea that complexity comes not from complexity but from simplicity. And the hidden promise here is that, while we could probably not master forces of sufficiently great complexity, we could one day master a few simple forces, or better yet just one simple idea. We might become Creators ourselves. The quest for God then has become a quest to become God ourselves.

Stephen Wolfram's "New Kind of Science", to the extent I could understand it, likewise proceeds from a faith that simplicity will be found to render complexity. In fact, carried to its logical conclusion, his theory can be understood to imply that by writing a few simple computer commands one could duplicate even something as complex as the Universe. There are obviously many problems with an idea this grandiose and many people who understand what he's talking about far better than I ever will have done a rather thorough job pointing them out. But that doesn't stop his book from being immensely appealing. It has a number of things going for it, some which we don't think about where scientific literature is concerned: (1) It's huge. It's just a big book. One feels it must be important just because of its heft. (2) The thesis is audacious enough and stated so unequivocally as to justify its bigness. The author is after big game here and has brought a big gun. (3) It's lovely. Not only does Mr. Wolfram write with a general public readership in mind but the book is also lavishly illustrated. It's a book that wants to be read. (4) By referring to that ancient metaphor, of simplicity and a moment of Creation, and by his implied promise, that men can be as gods, Mr. Wolfram is savvily tapping into those powerful and time-tested understandings and motivations that have driven mankind for millennia now. I've no idea whether the specific case that he makes is correct--cellular automata are Greek to me--but the general case is what we all of us want to believe, that life is really pretty simple if you trace it back to the start, that someone did in fact start it in motion, and that therefore life has a scheme it's following, some rules, a purpose. What he's really saying is that: "In the beginning was the Word..." That's powerful stuff.


(Reviewed:)

Grade: (A+)

  

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Science
Stephen Wolfram Links:

    -Stephen Wolfram: Official Web Site
    -AUDIO INTERVIEW: with Stephen Wolfram (Science Friday, July 5, 2002, NPR)
    -AUDIO INTERVIEW: with Stephen Wolfram (Diane Rehm, September 16, 2002, NPR)
    -INTERVIEW: QUESTIONS FOR STEPHEN WOLFRAM: Complexity Made Simple (LOCH ADAMSON, 7/07/02, NY Times Magazine)
    -INTERVIEW: Is this man bigger than Newton and Darwin?: British physicist Stephen Wolfram tells Graham Farmelo why his new book, already number one on Amazon.com, will revolutionise science (Daily Telegraph, 15/05/2002)
    -Stephen Wolfram - New Kind of Science: Alternative Views
    -PROFILE: Did This Man Just Rewrite Science? (DENNIS OVERBYE, 6/11/02, NY Times)
    -PROFILE: A Man Who Would Shake Up Science (EDWARD ROTHSTEIN, May 11, 2002, NY Times)
    -PROFILE: The Man Who Cracked The Code to Everything ...: ... But first it cracked him. The inside story of how Stephen Wolfram went from boy genius to recluse to science renegade. (Steven Levy, June 2002, Wired)
    -PROFILE: God, Stephen Wolfram, and Everything Else (Michael S. Malone, 11.27.00, Forbes ASAP)
    -PROFILE: Transcending Equations (JIM HOLT, December 9, 2001, NY Times Magazine)
    -PROFILE: Physicist: Programs run the universe (Stephen Shankland, November 21, 2002, ZDNet News)
    -ESSAY: Reflections on Stephen Wolfram's "A New Kind of Science" (Ray Kurzweil, KurzweilAI.net)
    -ESSAY : Kurzweil on Wolfram: The noted scientist finds plenty to mull and admire in A New Kind of Science but says it's "only partly correct" (Raymond Kurzweil, MAY 17, 2002, Business Week)
    -ESSAY: What's So New in a Newfangled Science? (GEORGE JOHNSON, 6/16/02, NY Times)
    -ESSAY: Blinded by Science: Explaining the media's obsession with Stephen Wolfram's A New Kind of Science. (Jordan Ellenberg, July 2, 2002, Slate)
    -ESSAY: The Physicist and the Abalone Diver: The difference between the creators of two new theories of science reveals the social nature of the scientific process (Michael Shermer, October 2002, Scientific American)
    -ESSAY: STEPHEN WOLFRAM AND CELLULAR AUTOMATA REVISITED (Brian Grainger)
    -ESSAY: Stephen Wolfram's Simple Science: Will his radical idea -- that all phenomena are programmed by basic rules -- revolutionizewhat's taught in classrooms and practiced in labs? (Michael Arndt, MAY 17, 2002, Business Week)
    -ESSAY: Is Science Unveiling Rules of Design?: Stephen Wolfram and Cellular Automata (The evolution of Truth)
    -ESSAY: Universality and Complexity in Cellular Automata
    -Understanding “A New Kind of Science” by Stephen Wolfram (SOFTWARE BY CHARLES PLATT)
    -ARCHIVES: "stephen wolfram" (Find Articles)
    -REVIEW ARCHIVE: A Collection of Reviews of ANKOS and Links to Related Work (W. Edwin Clark, eclark@math.usf.edu)
    -REVIEW: of A New Kind of Science (George Johnson, NY Times Book Review)
    -REVIEW: of A New Kind of Science (Michael J. Behe, First Things)
    -REVIEW: of A New Kind of Science (John Derbyshire, National Review)
    -REVIEW: of A New Kind of Science (David Appell, Salon)
    -REVIEW: of A New Kind of Science (Greg Egan)
    -REVIEW: of A New Kind of Science (Steven Weinberg, NY Review of Books)
    -REVIEW: of A New Kind of Science (Chris Lavers, The Guardian)
    -REVIEW: of A New Kind of Science (Philip Ball, The Observer)
    -REVIEW: of A New Kind of Science (Keay Davidson, SF Chronicle)
    -REVIEW: of A New Kind of Science (
    -REVIEW: of A New Kind of Science (
    -REVIEW: of A New Kind of Science (
    -REVIEW: of A New Kind of Science (Margaret Werthheim, LA Weekly)
    -REVIEW: of A New Kind of Science (Brian Hayes, American Scientist)
    -REVIEW: of A New Kind of Science (Ben Goertzel, EXTROPY: Journal of Transhumanist Solutions)
    -REVIEW: of A New Kind of Science (AzTex, kuro5hin.org)

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